The above picture shows some Decimal Tiles available for overhead projectors from www.enasco.com. Enasco also have a range of Percentage and Fractions tiles for sale on their Math Resources website.
We need to be able to convert Percentages to Decimals to obtain “Multiplying Factors” for mathematics questions.
For example, if there is a Discount of 25% on an item, then we can multiply the item’s price by 0.25 to work out the dollar amount of Discount.
How did we know that 25% equals Decimal 0.25 ?
We worked out the value of 0.25 by moving the decimal place of 25.% two places to the left, which is the same as dividing 25 by 100 on a calculator.
This lesson is all about Converting Percentages into Decimals
How to Convert to Decimal Values
Changing a Percentage value into a decimal value involves dividing the Percentage by 100.
This can be very easily done using a calculator.
Without using a calculator converting is still a simple process.
All we need to do are the following steps.
Image Copyright 2012 by Passy’s World
Converting to Decimal Values
The following examples show the main types of questions that involve changing a Percentage into its Decimal quivalent value.
Image Copyright 2012 by Passy’s World
Video on Percent to Decimal
The following video by Your Teacher .com and shows how to move the decimal point 2 places to the left to make a percent into a decimal.
Video on Percentages to Decimals
The following video by Khan Academy shows how to move the decimal point 2 places to the left to make any percent value into a decimal.
In this Time Trial activity, we type the answer in the answer box and then press enter, (or click the check box). We are then given immediate feedback about our answer. At the end of the time we get a % accuracy score for our work.
If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address.
Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.
To find out exactly how free subscription works, click the following link:
If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown in the right hand side bar of this page.
Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.
According to the National Electronic Injury Surveillance System (NEISS), Ankle Injuries in Soccer make up 18.2% of all injuries, and are one and half times higher than knee injuries.
Source: http://www.soccer-training-guide.com
What Fraction of soccer injuries are Ankle Injuries ?
To work this out we need to realise that % means / 100 .
So if we divide 18.2 % by 100, this should give the answer.
To divide by 100, we simply multiply by 1 / 100.
This gives 18.2 / 100 but this answer needs simplifying.
We need to multiply top and bottom by 10 to remove the decimal, then divide to simplify.
18.2 / 100 X 10 / 10 = 182 / 1000 divided by 2 = 91 / 500.
Our final fraction answer is that 91 out of every 500 soccer injuries are ankle injuries.
91 is fairly close to 100, so we could say 100 out of 500, which means that one out of every five injuries in soccer are ankle injuries.
If you are not good with fractions then use a Calculator.
On the Calculator do: 18.2 divided by 100 to get 0.182.
Then use your Calculator’s Decimal to Fraction converter button (usually 2nd funtion then F arrow D button F<>D on many calculators).
Lesson Overview
In this lesson we cover converting Percentage Values to Fractions, including simplifying fraction answers by reducing down.
Three types of Percentages will be converted to Fractions:
1) Whole Number Percentages
2) Percentages Containing Fractions
3) Percentages Containing Decimals
In all three cases the basic procedure is the same:
– Multiply the given item by 1/100, and then
Simplify to get the final Fraction answer.
Or if using a Calculator:
– Divide the given item by 100 and then
use Decimal to Fraction converter button if necessary.
Percent to Fractions Online Converters
The above two calculators can be found at the following links, and work as shown above.
Housing Loan Interest Rates often contain Fractional Percentages. So if we want to work out what Fraction of a $400 Payment is going to be Interest, we need to be able to convert the Interest Rate to a Fraction.
For a Loan with an Interest Rate of 12 and 1/4 % we do
12 and 1/4 = [(4×12 + 1) / 4] X (1/100)
= (49/4) X (1/100)
= 49 / 400
So for a $400 Payment, $49 of the total $400, is Interest Money we have to pay.
Our $400 Payment only pays $351 off our Loan Debt, and the other $49 is given to the Lending Institution as Interest Money.
Here are some more examples that contain Fractional Percents.
We should memorize that 33 and 1/3 percent = the fraction 1/3 .
However, if we did not remember, we can convert by these steps:
– Make an Improper Fraction for Mixed Numbers
– Multiply our Fraction by 1/100
– Simplify our Answer
To Convert 33 and 1/3 % we do:
33 and 1/3 = [(3×33 + 1) / 3] = 100/3
(100/3) X (1/100) = 100/300 (Divide by 100) = 1/3
So 33 and 1/3 % as a fraction is 1/3.
If we have a Fraction Percentage like 5/8 % to convert we do the following:
– Multiply our Fraction by 1/100
– Simplify our Answer
For 5 / 8 % we do this:
(5/8) X (1/100) = 5/800 (Divide by 5) = 1/160
and another example is the fractional percent 1/4 %
(1/4) x (1/100) = 1/400
If you want to use a Calculator the Steps are:
– Use the a/b or A b/c button to enter the given Fraction
– Do not press the % button at all !
– Divide by 100 (Calculator should give Fraction Answer).
Converting Fraction Percentages – SUMMARY
Image Copyright 2012 by Passy’s World
Converting Decimal Percentages
Image Source: http://www.inthesetimes.com
If unemployment goes up by 0.5% then how many extra unemployed people will there be ?
This question is best answered by converting 0.5% to a fraction.
Then we can figure out how many extra people per 100, or 200, or 500, or 1000 there will be.
The working is: 0.5% = 0.5 / 100 = (0.5 x 10) / (100 x 10)
= 5 / 1000 (Divided by 5) = 1 / 200 .
This means that when unemployment goes up by 0.5%, there will be One extra jobless person for every 200 existing unemployed people.
For decimal percentages with one number after the decimal point, we have to multiply top and bottom by 10.
For decimal percentages with two numbers after the decimal point, we have to multiply top and bottom by 100.
An example of a two decimal places percentage is 1.55 %
175 / 10 000 (Divided by 5) = 35 / 2000 (Divided by 5) = 7 / 400 .
On a Calculator for Decimal Percentages we do:
– Given % value divided by 100
– Use the Decimal to Fraction F<>D button to get final answer.
Converting Decimal Percentages – SUMMARY
To convert decimal percentages there is an extra step of multiplying by either 10 for one decimal place, or by 100 for two decimal places.
We then always simplify our resulting fraction if there is a number that goes into both the top and bottom of the fraction.
Image Copyright 2012 by Passy’s World
Video on Percentages to Fractions
Watch the first five minutes of this video which is all about converting Percents to Fractions.
Video on Improper Fractions to Mixed Numbers
This video shows how to convert Improper Fractions to Mixed Numbers.
We need to do this whenever the original given Percentage we are converting is bigger than 100%.
Video on Common Percents and Fractions
The following video reviews the common Fractions and Percentages that we covered in the “Introduction to Percentages” lesson.
Percentages to Fractions “Mission Magnetite” Game
Mission Magnetite involves Fractions and Percents.
In this fun game we click a percent first into it’s bottom circle, and then click it’s equivalent fraction, and then into the last bottom circle the appropriate drawing. It is a race against time to complete the puzzle before the rocket fills with fuel.
Percentages to Fractions – “Private Investigator” Game
In this game we solve the mystery of the burgled bank vault with Percentage P.I. Visually we locate percent values on Pie Charts and learn the fractions associated with percentages.
If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address.
Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.
To find out exactly how free subscription works, click the following link:
If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown in the right hand side bar of this page.
Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.
If there is a 50% off sale on at the store, most people will realize that everything is half its original price.
50% (or 50 percent) is equal to one half or ½ or 0.5
If 4 out of 5 people who visit the store buy at least one item, then the proportion of buyers is 4/5, or four fifths, or 80%.
How did we work out that 4/5 is 80% ?
To make any fraction a percentage we need to do top divided by bottom, and then multiply by 100. (4 divided by 5 x 100 on a calculator should give 80%).
Don’t worry too much about all that right now, because we will do a whole separate lesson on changing fractions to percents.
Percent simply means out of 100 or /100.
80% means 80 out of every 100 which can also be written as 80/100.
In countries like the USA and Australia, if we have 80 cents, then we have 80% of a dollar.
We would only need another 20 cents (or 20%) to get ourselves a full dollar.
Introductory Video About Percents
Watch the following video which introduces percents in less than three minutes.
Common Percent Values
The following common Percentage Values need to be memorised.
It is very useful to have an idea of what fraction of a whole amount any given percentage is.
Image Copyright 2012 by Passy’s World
Online Lesson on Percentages
Do the following lesson from “Math Goodies” and then try the online test at the bottom of the page.
This does advance into areas we have not looked at yet, and so if it is too hard, then skip it until you have learned a bit more about Percentages.
Click the following link to do the free online lesson.
This short video is a little bit out there. It involves Percentages and their Decimal equivlanets, and covers the basic out of 100 concept.
Visualizing Percents Online Game
We recommend playing the following game which greatly helps to visualise Percentage Amounts.
This is not so much of a game as an activity, where percentages can be viewed as part of a Pizza, a number of people, how full a jug is, or how much chocolate is left.
To start the game, click on one of the bottom icons such as Pizza, People, Jug, or Chocolate Bar.
We then simply click down and hold the mouse button, and then drag the % value from the right hand table, into the black action box, and the picture then changes to show us the percent amount we have chosen.
In a recent survey 25 out of 28 students in a class said that they had used Facebook. Eight girls sitting together at a fast food restaurant were also surveyed and 7 out of 8 had used Facebook.
Which group had a greater proportion of people who had used Facebook ?
To answer this question we would need to know if 25/28 is a bigger fraction than 7/8.
This is not at all easy to figure out.
To get an answer for situations like this we use Percentages.
25/28 as a Percentage is 25/8 x 100 = 89%.
7/8 as a Percentage is 7/8 x 100 = 88%.
89% is larger than 88% (just like 89 is bigger than 88), and so the class of students had a very slightly higher proportion of people who had used Facebook.
Percentages are often used for comparing items such as survey results.
Online Quiz One on Percentages
This multiple choice quiz can be done Online, or you can click the Download button and Download it as a PDF or a DOC.
There are three levels of Quizes that can be done, and each of the three quizes has 10 questions.
If the Quiz is done online then a final score and fully worked answers are given after the quiz is completed.
If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address.
Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.
To find out exactly how free subscription works, click the following link:
If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown in the right hand side bar of this page.
Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.
The following example shows how we can use Ratios for sharing out amounts.
Also shown is the standard approach and working out steps for doing these types of mathematics questions.
Image Copyright 2012 by Passy’s World
As agreed by the three friends, the winnings of $ 120 000 need to be shared amongst them in the same ratio as the money they each contributed towards the ticket.
Image Copyright 2012 by Passy’s World
We now work out from the 20 parts total, how much “One Part” is worth.
After we know what one part is, it is then just simple multiplication to work out what share of the total amount each person gets.
Image Copyright 2012 by Passy’s World
We have our sharing amount answers, and it is always a good idea to check these answers to make sure that they are correct.
There are two levels of checking we can do.
These involve checking the Total of the Amounts, and then checking the Ratio of the Amounts.
Image Copyright 2012 by Passy’s World
Image Copyright 2012 by Passy’s World
Because both checks have been successful, we can be 100% sure that our sharing Answers are correct.
Video about Ratio Sharing
Watch the following video which is about sharing out items in given ratios.
This video uses the notion of “rounds” which might appear a bit different to our example lottery question, but is actually the same.
The total “rounds” are simply the “Total Parts”, and so the video presenter gives so many rounds to each person depending on their share of the ratio.
Steps for Working Out Sharing Questions
The previous example has shown the steps that we need to do to work out a Ratios question which involves sharing amounts.
We use these exact same steps for working out questions that involve dividing up amounts.
Image Copyright 2012 by Passy’s World
Steps for Checking Sharing Questions
As shown at the end of the Lottery example, there were two checks that we need to do for Ratios Sharing Questions.
The first check involves checking that the answer amounts all add up to exactly match the original amount being shared.
The second check involves checking that the Ratio of the answer amounts exactly matches the original sharing ratio.
Image Copyright 2012 by Passy’s World
Ratios Sharing Examples
The following examples show how to do questions which involve dividing up amounts, or sharing amounts.
In each example we follow the standard working out steps:
– Find the Total Number of Parts in the Ratio
(Do this by adding up all the number values in the given Ratio to get a Total
– Amount for One Part = (Total Amount being shared) / Total Number of Parts in Ratio
(This tells us what one part is worth)
– Each Share = its Ratio Number x Amount for One Part.
Although not shown on all of our examples, remember that checking our amswer amounts is just as important as doing the working out steps.
The standard Answer Checking Steps are as follows:
– Check all the shares add up to the original given Amount
– Check the Ratio of the Shares simplifies to be the same as the Original Given Ratio.
If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address.
Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.
To find out exactly how free subscription works, click the following link:
If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown in the right hand side bar of this page.
If you are a subscriber to Passy’s World of Mathematics, and would like to receive a free PowerPoint version of this lesson valued at $4.99, but 100% free to you as a Subscriber, then email us at the following address:
Please state in your email that you wish to obtain the free subscriber copy of the “Sharing Using Ratios” PowerPoint.
Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.
But what if we have 5 people coming over for a curry dinner?
How can we adjust our recipe for 4 people, so that it can feed 5 people ?
We need to use the Mathematics of Ratios !
We need to increase our Recipe in the Ratio of 5 : 4
This makes perfect sense, because Ratios are often used for comparing.
The Ratio of 5 : 4 means we are now feeding 5 people as compared to the recipe’s 4 people.
Remembering that all Ratios can be written as Fractions, we can increase our Recipe by 5 : 4 by simply multiplying all of the Ingredients by 5/4 or one and one quarter.
To Increase a quantity in the Ratio of “b : a” we multiply the quantity by the fraction “b/a”
Let’s consider the Chicken Curry Spice Mix Quantities.
For Four People we need the following Spice amounts:
1 heaped teaspoon of fennel seeds
2 teaspoons of crushed ground black peppercorns
1 heaped teaspoon of dried red chilli flakes
1/4 heaped teaspoon of ground cardamom seeds
1 flat teaspoon of ground Nutmeg
For Five People we need to multiply all these amounts by 5 / 4
5/4 x 1 = One and one quarter heaped teaspoon of fennel seeds
5/4 x 2 = 10/4 = two and a half teaspoons of black peppercorns
5/4 x 1 = One and one quarter heaped teaspoon of chilli flakes
5/4 x 1/4 = 5/16 heaped teaspoon of ground cardamom seeds **
5/4 x 1 = One and one quarter flat teaspoon of ground Nutmeg
** 5/16 teaspoon of ground cardamom seeds is going to be very hard to measure, and is only 1/16 of a teaspoon extra compared to the original recipe. For this reason we would probably just leave the Cardamom as 1 heaped quarter teapsoon.
As well as the ratio mathematics, we also need to use some common sense when scaling up and down recipes!
So Problem Solved! Five people will be able to come over for dinner and enjoy our delicious chicken curry.
Image Copyright 2012 by Passy’s World
Note that we can also Decrease Ratios.
For example if only three people were coming to dinner, we could decrease down our recipe in the Ratio 3 : 4 by multiply all our recipe quantities by 3/4.
Increasing and Decreasing Ratios
To Increase a one teaspoon quantity of Spice in the Ratio of “5 : 4”
we multiplied the quantity by the fraction “5/4”.
The answer came out as “one and one quarter teaspoons”, which was a bigger amount than what we started with.
Image Copyright 2012 by Passy’s World
To Decrease an amount in a given Ratio, we need to multiply by a fraction that is less than one.
For example, in scaling down a recipe for four people into a recipe for 3 people, we would use the ratio of 3 : 4 which means we would multiply all our recipe amounts by 3/4.
This will decrease all of the recipe quantities to three quarters of what they were originally.
Image Copyright 2012 by Passy’s World
Increasing and Decreasing with Ratios Examples
In the following examples we increase, or decrease, the given amounts by multiplying by the ratio given in the question.
These are fairly easy questions, all we have to do each time is:
Multiply the given numeric Item by the Ratio given in the question
If you enjoyed this post, why not get a free subscription to our website. You can then receive notifications of new pages directly to your email address.
Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.
To find out exactly how free subscription works, click the following link:
If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown in the right hand side bar of this page.
Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.
Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.
Visitor Statistics
User Feedback
We love hearing from our Users. Email us at the hotmail address shown below with any comments, ideas for articles, or to report any broken links or blank images on our pages.
